3x^2+12x=-3

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Solution for 3x^2+12x=-3 equation:


Simplifying
3x2 + 12x = -3

Reorder the terms:
12x + 3x2 = -3

Solving
12x + 3x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 12x + 3x2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 12x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(1 + 4x + x2)' equal to zero and attempt to solve: Simplifying 1 + 4x + x2 = 0 Solving 1 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x + x2 = 0 + -1 4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 4x + x2 = -1 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1 + 4 Reorder the terms: 4 + 4x + x2 = -1 + 4 Combine like terms: -1 + 4 = 3 4 + 4x + x2 = 3 Factor a perfect square on the left side: (x + 2)(x + 2) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 2 = 1.732050808 Simplifying x + 2 = 1.732050808 Reorder the terms: 2 + x = 1.732050808 Solving 2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.732050808 + -2 x = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 x = -0.267949192 Simplifying x = -0.267949192

Subproblem 2

x + 2 = -1.732050808 Simplifying x + 2 = -1.732050808 Reorder the terms: 2 + x = -1.732050808 Solving 2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.732050808 + -2 x = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 x = -3.732050808 Simplifying x = -3.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.267949192, -3.732050808}

Solution

x = {-0.267949192, -3.732050808}

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